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| Author | : Simo Särkkä |
| Publisher | : Cambridge University Press |
| Total Pages | : 255 |
| Release | : 2013-09-05 |
| Genre | : Computers |
| ISBN | : 110703065X |
A unified Bayesian treatment of the state-of-the-art filtering, smoothing, and parameter estimation algorithms for non-linear state space models.
| Author | : Simo Särkkä |
| Publisher | : Cambridge University Press |
| Total Pages | : 438 |
| Release | : 2023-05-31 |
| Genre | : Mathematics |
| ISBN | : 1108912303 |
Now in its second edition, this accessible text presents a unified Bayesian treatment of state-of-the-art filtering, smoothing, and parameter estimation algorithms for non-linear state space models. The book focuses on discrete-time state space models and carefully introduces fundamental aspects related to optimal filtering and smoothing. In particular, it covers a range of efficient non-linear Gaussian filtering and smoothing algorithms, as well as Monte Carlo-based algorithms. This updated edition features new chapters on constructing state space models of practical systems, the discretization of continuous-time state space models, Gaussian filtering by enabling approximations, posterior linearization filtering, and the corresponding smoothers. Coverage of key topics is expanded, including extended Kalman filtering and smoothing, and parameter estimation. The book's practical, algorithmic approach assumes only modest mathematical prerequisites, suitable for graduate and advanced undergraduate students. Many examples are included, with Matlab and Python code available online, enabling readers to implement algorithms in their own projects.
| Author | : Lawrence D. Stone |
| Publisher | : Springer Nature |
| Total Pages | : 124 |
| Release | : 2023-05-31 |
| Genre | : Computers |
| ISBN | : 3031322428 |
This book provides a quick but insightful introduction to Bayesian tracking and particle filtering for a person who has some background in probability and statistics and wishes to learn the basics of single-target tracking. It also introduces the reader to multiple target tracking by presenting useful approximate methods that are easy to implement compared to full-blown multiple target trackers. The book presents the basic concepts of Bayesian inference and demonstrates the power of the Bayesian method through numerous applications of particle filters to tracking and smoothing problems. It emphasizes target motion models that incorporate knowledge about the target’s behavior in a natural fashion rather than assumptions made for mathematical convenience. The background provided by this book allows a person to quickly become a productive member of a project team using Bayesian filtering and to develop new methods and techniques for problems the team may face.
| Author | : Michael C. Burkhart |
| Publisher | : ProQuest Dissertations Publishing |
| Total Pages | : 134 |
| Release | : 2019-05-26 |
| Genre | : Mathematics |
| ISBN | : |
Given a stationary state-space model that relates a sequence of hidden states and corresponding measurements or observations, Bayesian filtering provides a principled statistical framework for inferring the posterior distribution of the current state given all measurements up to the present time. For example, the Apollo lunar module implemented a Kalman filter to infer its location from a sequence of earth-based radar measurements and land safely on the moon. To perform Bayesian filtering, we require a measurement model that describes the conditional distribution of each observation given state. The Kalman filter takes this measurement model to be linear, Gaussian. Here we show how a nonlinear, Gaussian approximation to the distribution of state given observation can be used in conjunction with Bayes’ rule to build a nonlinear, non-Gaussian measurement model. The resulting approach, called the Discriminative Kalman Filter (DKF), retains fast closed-form updates for the posterior. We argue there are many cases where the distribution of state given measurement is better-approximated as Gaussian, especially when the dimensionality of measurements far exceeds that of states and the Bernstein—von Mises theorem applies. Online neural decoding for brain-computer interfaces provides a motivating example, where filtering incorporates increasingly detailed measurements of neural activity to provide users control over external devices. Within the BrainGate2 clinical trial, the DKF successfully enabled three volunteers with quadriplegia to control an on-screen cursor in real-time using mental imagery alone. Participant “T9” used the DKF to type out messages on a tablet PC. Nonstationarities, or changes to the statistical relationship between states and measurements that occur after model training, pose a significant challenge to effective filtering. In brain-computer interfaces, one common type of nonstationarity results from wonkiness or dropout of a single neuron. We show how a robust measurement model can be used within the DKF framework to effectively ignore large changes in the behavior of a single neuron. At BrainGate2, a successful online human neural decoding experiment validated this approach against the commonly-used Kalman filter.
| Author | : Harry L. Van Trees |
| Publisher | : Wiley-IEEE Press |
| Total Pages | : 951 |
| Release | : 2007-08-31 |
| Genre | : Technology & Engineering |
| ISBN | : 9780470120958 |
The first comprehensive development of Bayesian Bounds for parameter estimation and nonlinear filtering/tracking Bayesian estimation plays a central role in many signal processing problems encountered in radar, sonar, communications, seismology, and medical diagnosis. There are often highly nonlinear problems for which analytic evaluation of the exact performance is intractable. A widely used technique is to find bounds on the performance of any estimator and compare the performance of various estimators to these bounds. This book provides a comprehensive overview of the state of the art in Bayesian Bounds. It addresses two related problems: the estimation of multiple parameters based on noisy measurements and the estimation of random processes, either continuous or discrete, based on noisy measurements. An extensive introductory chapter provides an overview of Bayesian estimation and the interrelationship and applicability of the various Bayesian Bounds for both static parameters and random processes. It provides the context for the collection of papers that are included. This book will serve as a comprehensive reference for engineers and statisticians interested in both theory and application. It is also suitable as a text for a graduate seminar or as a supplementary reference for an estimation theory course.
| Author | : Simo Särkkä |
| Publisher | : Cambridge University Press |
| Total Pages | : 327 |
| Release | : 2019-05-02 |
| Genre | : Business & Economics |
| ISBN | : 1316510085 |
With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
| Author | : Arnaud Doucet |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 590 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 1475734379 |
Monte Carlo methods are revolutionizing the on-line analysis of data in many fileds. They have made it possible to solve numerically many complex, non-standard problems that were previously intractable. This book presents the first comprehensive treatment of these techniques.
| Author | : Huazhen Fang |
| Publisher | : |
| Total Pages | : 165 |
| Release | : 2014 |
| Genre | : |
| ISBN | : 9781321011265 |
Estimation of unknown quantities in a nonlinear dynamic system has been a challenge of great interest and importance, which is encountered in different research fields. Founded on a perspective of updating probabilistic belief on unknown quantities with observations, Bayesian analysis has provided a useful methodology and framework for construction of various estimation techniques. This dissertation presents a study of some new developments and applications of Bayesian estimation theory. Both filtering and smoothing will be considered --- the former concerns estimation of the present situation using measurements up until the present time, and the latter is about estimation of the past using all the measurements. In the dissertation, we investigate both state estimation and simultaneous input and state estimation. For the former, Bayesian filtering in a Gaussian context is discussed. We propose to use the radial basis function approximation as a desirable option to realize the Gaussian state filtering. We then improve the standard ensemble Kalman filter by introducing iterative optimization. Simultaneous input and state estimation has emerged as a new challenge. We extend the Bayesian methodology to deal with this problem and consider both filtering and smoothing cases. The Bayesian paradigms are built as a statistical foundation to fulfill this task, are built. On such a basis, we then develop a series of estimation methods using iterative optimization and Monte Carlo-based ensemble approaches. We further examine the link between our methods and the existing ones and analyze their properties especially in the linear case. The dissertation also studies application of estimation techniques to some real-world issues. We investigate real-time state-of-charge estimation for batteries, proposing an adaptive method based on multi-model state estimation. It allows for accurate estimation in the presence of uncertain or unknown variables and can promote the battery monitoring performance and operational safety potentially. The other application presented is oceanic flow field reconstruction. Flows exist everywhere in the ocean, playing a crucial role in many aspects of marine environment and biology. As part of a collaborative effort with Scripps Institution of Oceanography to build an original ocean observing system based on a group of drifters, we apply the simultaneous input and state estimation methods proposed to analyze the data collected by drifters to estimate the flow velocity and monitor the drifter's motion status. This work can be conducive to future endeavors in oceanographic research.
| Author | : Genshiro Kitagawa |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 265 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461207614 |
Smoothness Priors Analysis of Time Series addresses some of the problems of modeling stationary and nonstationary time series primarily from a Bayesian stochastic regression "smoothness priors" state space point of view. Prior distributions on model coefficients are parametrized by hyperparameters. Maximizing the likelihood of a small number of hyperparameters permits the robust modeling of a time series with relatively complex structure and a very large number of implicitly inferred parameters. The critical statistical ideas in smoothness priors are the likelihood of the Bayesian model and the use of likelihood as a measure of the goodness of fit of the model. The emphasis is on a general state space approach in which the recursive conditional distributions for prediction, filtering, and smoothing are realized using a variety of nonstandard methods including numerical integration, a Gaussian mixture distribution-two filter smoothing formula, and a Monte Carlo "particle-path tracing" method in which the distributions are approximated by many realizations. The methods are applicable for modeling time series with complex structures.
| Author | : Kostas Triantafyllopoulos |
| Publisher | : Springer Nature |
| Total Pages | : 503 |
| Release | : 2021-11-12 |
| Genre | : Mathematics |
| ISBN | : 303076124X |
Bayesian Inference of State Space Models: Kalman Filtering and Beyond offers a comprehensive introduction to Bayesian estimation and forecasting for state space models. The celebrated Kalman filter, with its numerous extensions, takes centre stage in the book. Univariate and multivariate models, linear Gaussian, non-linear and non-Gaussian models are discussed with applications to signal processing, environmetrics, economics and systems engineering. Over the past years there has been a growing literature on Bayesian inference of state space models, focusing on multivariate models as well as on non-linear and non-Gaussian models. The availability of time series data in many fields of science and industry on the one hand, and the development of low-cost computational capabilities on the other, have resulted in a wealth of statistical methods aimed at parameter estimation and forecasting. This book brings together many of these methods, presenting an accessible and comprehensive introduction to state space models. A number of data sets from different disciplines are used to illustrate the methods and show how they are applied in practice. The R package BTSA, created for the book, includes many of the algorithms and examples presented. The book is essentially self-contained and includes a chapter summarising the prerequisites in undergraduate linear algebra, probability and statistics. An up-to-date and complete account of state space methods, illustrated by real-life data sets and R code, this textbook will appeal to a wide range of students and scientists, notably in the disciplines of statistics, systems engineering, signal processing, data science, finance and econometrics. With numerous exercises in each chapter, and prerequisite knowledge conveniently recalled, it is suitable for upper undergraduate and graduate courses.
